Question

I'm very confused help....

I really don't understand how to prove trig identities can someone please explain thoroughly. Please help me with one or all below! ( Whoever explains all gets brainliest)


a) cosx / sin x = 1 / tan x

b) sin^2x / tan^2x = 1 - sin^2x

c) cosx = sin^3x / tanx + cos^3 x


Thanks!

Answer 1

Step-by-step explanation:

LHS = Left Hand Side ; RHS = Right Hand Side

a) RHS = 1/ tan x

= 1/ (Sin x/Cos x)

= Cos x/Sin x

= LHS

b) LHS = Sin^2 x / tan^2 x

= Sin^2 x / (Sin^2 x/Cos^2 x)

=( Sin^2 x * Cos^2 x) / (Sin^2 x)

= Cos^2 x

= 1 - Sin^2 x (Because sin^2 x + cos^2 x = 1)

= RHS

c) RHS = Sin^3 x / tan x + Cos^3 x

= Sin^3 x / (Sinx/Cosx) + Cos^3 x

= (Sin^3 x * Cos x)/Sin x + Cos^3 x

= Sin^2 x * Cos x + Cos^3 x

= Cos x (Sin^2 x + Cos^2 x)

= Cos x *(1) {Because, Sin^2 x + Cos^2 x = 1}

= Cos x

= LHS